Is it possible, to modify the speed of the (keyboard) cursor if you hold one key down.? I think it is too slow and I want to tweak it, to let the cursor move at a higher speed. This might be something for the config.txt.

On Mac OS X it's controlled by OS

System Preferences > Keyboard > Key Repeat
System Preferences > Keyboard > Delay Until Repeat

What platform are you running on?

Alternatively, a common shortcut (at least on windows) seems to be Ctrl + [Arrow Keys] to jump from 'word' to 'word'. This appears to also work in Pico-8's editor too, although I don't if the shortcut is the same on Mac or Linux. Hope that's helpful.
Edit: Woops looks like I mis-remembered. Apparently Ctrl + (left/right) Arrow Key jumps every four chars, not every word. [insert smacking head on desk here]

It seems that internally, the key repeat now works the same as BTNP() does. This is a recent change.

On macOS that is definitely not the case.

I can dial down the repeat rate in System Preferences and in pico8 it goes slow, and then dial it back up and it goes fast. I do not even have to restart pico8 to see the changes.

Witness:
https://vimeo.com/170317730

Are you guys on Windows or Linux?

Hm, I am on OS-X 10.11.4 and Pico-8 0.1.6 and I can't see any change in speed when I modify keyboard-settings, so I go with @solars answer more... =)

Is there a way to change BTNP?

Hmm, I am on OSX 10.11.5 and Pico-8 0.1.6

Aha, there was a slight misunderstanding, or better an interesting behavior.

The Key-Repeat speed works like you showed in the video, but this is not true for the movement of the cursor using the cursor keys. This speed is somehow fixed and seems, that it can't be modified.

Aha! Good spot.

Yeah I noticed this as well. Good call bringing it up here!